Question

HELP HELP HELP
Just a quick question for 100 points! :)

Answer 1

see attached graphs

Explanation:

Transformations

For a > 0

`f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}`

`f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}`

`f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}`

`f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}`

`y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a`

`y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: (1)/(a)`

`y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}`

`y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}`

Parent function:
`f(x) = x`

Each transformation is a transformation of the parent function only:

Translation of 4 units down

`\implies f(x)-4=x-4`

`\implies y=x-4`

A stretch by a factor of 3

`\implies 3f(x)=3x`

`\implies y=3x`

A reflection and a translation 1 unit up

`\implies f(-x)+1=-x+1`

`\implies y=-x+1`